Name:_________________Date:__________ 1
Notes on Factoring: Butterfly Method
Factors are
numbers or
expressions
that are
multiplied to
get another
number or
expression.
We are trying
to find what
binomial
factors
multiply to
equal the
polynomial.
This method will work when
factoring x 2  bx  c or
ax 2  bx  c
a ∙c x2
2
ax
factor1 x
ax 2
factor 2  x
bx
Some examples
2
x
 7 x  10
1) Factor
a = 1, b = -7 and c = 10
The factors are the simplified
terms
Name:_________________Date:__________ 2
Notes on Factoring: Butterfly Method
2) Factor x 2  4 x  12
a = 1, b = 4, c = -12
The factors are
3) Factor
4 x 2  4 x  15
a = 4, b = -4 and c = -15
The factors are the simplified
terms
Name:_________________Date:__________ 3
Notes on Factoring: Butterfly Method
4) Factor 5x 2  26x  5
a = 5, b = -26, c = 5
The factors are
5) Factor
6x 2  9 x  15
Factor out 3 first 3(2 x  3x  5)
2
The factors are the simplified
terms
Name:_________________Date:__________ 4
Notes on Factoring: Butterfly Method
Try: Factor 2 x 2  3x  5
a= ,b=
,c=
The factors are ______________
5) Factor
3x 2  x  10
The factors are
________________
Name:_________________Date:__________ 5
Notes on Multiplying: FOIL and BOX Methods
Multiplying Binomials:
FOIL
Outer
Last
(2x + 3)(x – 6)
First
Inner
F
O
I
L
= 2x(x) + 2x(-6) + 3(x) + 3(-6)
= 2x2 -12x + 3x – 18
= 2x2 – 9x-18
Area Model
(4x2 + 5)(3x2 – 2)
4x2
3x2
-2
=
=
+5
12x4
15x2
-8x2
-10
12x4 + 15x2 – 8x2 – 10
12x4 + 7x2 - 10
Name:_________________Date:__________ 6
Notes on Mult Polynomials : Distributive Prop.
Multiplying (x + 3)(x2 +2x+ 4)
Have to distribute:
x(x2 +2x+ 4) + 3(x2 +2x+ 4)
= x  2 x  4 x  3x  6x  8
3
2
2
x 3  5x 2  10x  8
Area Method
Multiply (x + 4)(x2 + 2x – 3)
x2
Create a box
x
+4
= x3 + 6x2 + 5x – 12
+2x
-3
x3
2x2
-3x
4x2
8x
-12
Name:_________________Date:__________ 1
Notes on Multiplying: FOIL and BOX Methods
Name:_________________Date:__________ 1
Notes on Multiplying: FOIL and BOX Methods